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Abstract Algebra

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Irreducibility of Polynomials and p-th Roots of Unity

ABSALG-1D8JZW

Let $p\ge 2$ be a prime number. Which of the following expressions are polynomials in ${\mathbb Q}[x]$ that are irreducible over ${\mathbb Q}$?

Select ALL that apply

A

$x^p-1$

B

$((x+1)^p-1)/x$

C

$(x^p-1)/(x-1)$

D

$x^p-p$

E

$x^{2p}-p^2$